ON THE DIFFICULT INTERPLAY BETWEEN LIFE, "COMPLEXITY", AND MATHEMATICAL SCIENCES

NICOLA BELLOMO; KNOPOFF DAMIAN; JUAN SOLER

MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2013 vol. 23 p. 1861 - 1913

0218-2025

This paper presents a revisiting, with developments, of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions. The approach is based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games. The basic idea consists in looking for ageneral mathematical structure suitable to capture the main features of living, hence complex, systems. Hopefully, this structure is a candidate towards the challenging objective of designing a mathematical theory of living systems. These topics are treated in the first part of the paper, while the second one applies it to specific case studies, namely to the modeling of crowd dynamics and of the immune competition.